The general idea is a very good one (and has been thought of independently by a number of people.) But using a world map (in particular the one Adam showed in his lovely images) is not optimal, because so many colors in different parts of the initial globe are identical or almost so. Using a face may be better but also has the disadvantage of requiring us to distinguish the left half from the right half. At least we know meromorphic functions preserve orientation, so this shouldn't be extremely hard, but still requires a disambiguation that may not be particularly helpful. (Though for certain functions having a real period equal to the width of the face, it could be especially helpful.) But in general, an asymmetrical familiar picture may be most helpful. One common device is to use a square with left->right showing one gradient, and bottom->top showing another. For example, left->right might show the colors between white and red, and bottom->top might show dots of increasing radius. Or similarly there could be one gradient showing angle (perhaps the circular "spectrum" of saturated colors) and another one (e.g., saturation) to show increasing radius. These abstract gradients aren't necessarily viscerally more helpful than a familiar picture of something, but they do aid in quickly identifying real and imaginary components, or radius and angle, of the function values. --Dan On 2013-01-27, at 9:47 AM, Marc LeBrun wrote:
="Adam P. Goucher" <apgoucher@gmx.com> Tim Large suggested an idea
Nice! You might also try, instead of a world map, using a human face as the base image, making expressions of expressions, so to speak.